Which word in this sentence is a participle?
the frightened cat climbed to the top of the tree.
a. cat
b. top
c. frightened
d. climbed

i don't see it in your profile.                                                  

the best sentence that shows the best placement for the modifier "on the ice" is the one which contains it in the end of the sentence or in its beggining followed by a comma, that indicates it works as adverbial, dislocated in the sentence.

the girl promptly slid on her rollers on the ice.

on the ice, the girl promptly slid on her rollers.